There is no admission that the background art disclosed in this section legally constitutes prior art.
Enantiomerically pure β-lactones are valuable small molecules that can be converted into a variety of chiral synthons for asymmetric synthesis.1 Because the [2+2] cycloaddition reaction between ketene and aldehydes affords β-lactones in one step, developing new catalytic methods for synthesizing β-lactones from ketene and aldehydes attracts much attention.1,2 
Quinidine-based catalysts. FIG. 1-Scheme 1 shows the enantioselective synthesis of β-lactone 5 from ketene 1 and chloral 3, catalyzed by quinidine (Q*).3 This formal [2+2] reaction entails a tandem aldol-lactonization process (from 2 to 4 to 5) to produce the β-lactone 5 in highly desirable enantiomeric purity (ee), but limited only to activated substrates. Significant research effort has been devoted to expanding the substrate scope of the [2+2] reaction.
Other catalysts. In addition to strategies for synthesizing bi-cyclic β-lactones from aldehyde acids,4 others have developed new catalytic methods to synthesize chiral β-lactones from aldehydes and substituted ketenes.5 Also, chiral Lewis bases (LB*) and chiral Lewis acids (LA*) were developed to synthesize β-lactones from pure ketenes.6a,6b Most recently, new catalytic systems have been developed for the [2+2] cycloaddition reaction between aldehydes and substituted ketenes.6c,6d,6e 
Lewis acid-Lewis base (LA*-LB*) bi-functional Co(II) catalysts. The inventor herein previously synthesized a (±)-Co(II)-LB bi-functional catalyst 6 from the (±)-diaminopropionic acid, and demonstrated the LB*-dependent asymmetric induction concept.7,9 The present inventor previously used a CoII-based bifunctional catalyst in a [2+2] cycloaddition reaction as a test reaction (FIG. 3A).7 The inventor herein also previously developed an empirical model for predicting the R/S absolute stereochemistry of LA*-LB* catalyzed reactions.9 
Described herein is a further development by the inventor that provides valuable chiral compositions and processes for producing them.